right hand rule

If the Riemann integral is considered as a measure of area under a curve, then the expressions f⁢(a+j⁢(b-an)) the of the rectangles, and b-an is the common of the rectangles.

The Riemann integral can be approximated by using a definite value for n rather than taking a limit. In this case, the partition is {[a,a+b-an),…,[a+(b-a)⁢(n-1)n,b]}, and the function is evaluated at the endpoints of each of these intervals. Note that this is a special case of a right Riemann sum (http://planetmath.org/RightRiemannSum) in which the xj’s are evenly spaced.